$J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 7x - 2$ and $ JT = 5x + 8$ Find $CT$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {7x - 2} = {5x + 8}$ Solve for $x$ $ 2x = 10$ $ x = 5$ Substitute $5$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 7({5}) - 2$ $ JT = 5({5}) + 8$ $ CJ = 35 - 2$ $ JT = 25 + 8$ $ CJ = 33$ $ JT = 33$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {33} + {33}$ $ CT = 66$